Existence and Fractional Inequalities for Hybrid $\rho$-Caputo Fractional Integro-Differential Equations with Non-Local Conditions

Abstract

This paper focuses on investigating the existence of solutions and fractional inequalities for a hybrid $\rho$-Caputo fractional differential equation accompanied by a non-local condition. By leveraging the Dhage fixed point theorem, we establish specific criteria that guarantee the existence of solutions for our problem. Furthermore, through the application of the $\rho$-Caputo derivative techniques, we illustrate various fractional inequalities.